Research & Scholarship

My research interests lie in Complex Geometry, Differential Geometry, Algebraic Geometry, Complex Analysis, Coding Theory, and Cryptography. I also have interests in Mathematics Education---particularly on innovative pedagogy, effective learning strategies, and different technologies used for instruction and assessment. I am also interested in ways to help increase participation of underrepresented groups and minorities in STEM fields.

Works and Publications:

• A. Álvarez, Z. Flores, A. Salerno, G. Terra Bastos. A Construction of Optimal Locally Recoverable Quasi-Cyclic Codes Using Constituent Codes. In preparation.

• A. Álvarez, M. Hunnell, J. Hutchens, E. Flapan, E. Lawrence, P. Lewis, C. Price, R. Vanderpool. Topological Symmetry Groups of the Generalized Petersen Graphs. Submitted. (Also see: arXiv:2402.08820.)

• A. Álvarez, G. Heier, F. Zheng. On projectivized vector bundles and positive holomorphic sectional curvature. Proc. Amer. Math. Soc. 146, no. 7, 2877–2882, 2018 (Also see arXiv:1606.08347.)

• A. Álvarez. On the positive holomorphic sectional curvature of projectivtized vector bundles over compact complex manifolds. Ph.D. Dissertation, 2016.

• A. Álvarez, A. Chaturvedi, G. Heier. Optimal pinching for the holomorphic sectional curvature of Hitchin’s metrics on Hirzebruch surfaces. Contemp. Math., 654:133–142, 2015. (Also see arXiv:1507.06629.)

Writing Contributions to the Profession:

• A. Álvarez. Reflections: Teaching Future Elementary School Teachers via Zoom. The Seaway Current: The Official Newsletter of the MAA Seaway Section, Volume 43 - Number 04, June 2020. (Link)

• A. Álvarez, M. Espanol, A. Faridani, C. Flores, A. Marr, E. Newman, J. McNulty, R. Nugent, A. Seneres, M. Shott, W. Y. Velez, E. Walker. The PCMI workshop for mentors: A weeklong workshop on diversity. Notices of the AMS , May 2018  (Link)

Grants Awarded:

• July 2023 - July 2026: AMS-Simons Research Enhancement Grants for Primarily Undergraduate Institution (PUI) Faculty Grant, PI

• July 2023 - July 2024: ERAU Faculty Innovative Research in Science and Technology (FIRST) Grant, Co-PI

• July 2023 - July 2024: MAA Tensor Women and Mathematics Grant (Renewal), Co-PI

• January 2023 - May 2023: ERAU Center for Teaching and Learning Excellence, Innovative Teaching Grant

• July 2022 - July 2023: MAA Tensor Women and Mathematics Grant, PI

• June 2019 - June 2020: SUNY Office of Diversity, Inclusion, and Equity Grant

Invited Talks:

• May 2023: Mathematical Pathways to an Excellent Future, UC Riverside (Plenary Speaker)

• May 2023: 2023 AMS Spring Western Sectional Meeting - AMS Special Session on Women in Math, Fresno State U.

• November 2022: Department of Mathematics Colloquium, Dnipro National University, Dnipro, Ukraine

• August 2022: The Eighth Annual Conference for the Exchange of Mathematical Ideas,  ERAU Prescott

• April 2022: ArizMATYC/MAA Southwestern Section Joint Conference, Arizona State U. Polytech

• February 2022: Latinx Mathematicians Research Community (LMRC) Colloquium

• December 2021: Embry-Riddle Aeronautical University Prescott Math Club

• April 2021: Mathematics Colloquium, Appalachian State University

• October 2020: Panel/Workshop: Coordinating Groupwork Remotely, MAA Seaway Section

• October 2019: Math Alliance Speaker Series, SUNY Potsdam

• March 2019: 2019 AMS Spring Central & Western Joint Sectional Meeting - AMS Special Session on Topics on the Interface of of Analysis and Geometry, U. Hawaii

• April 2018: Minorities In Mathematics Speaker Series (MIMSS), West Point - United States Military Academy

• January 2018: The 2018 Joint Math Meetings – AMS Special Session on Presentations by Scholars in the National Alliance for Doctoral Studies in the Mathematical Sciences, San Diego, CA

• November 2017: Math Alliance: 2017 National Field of Dreams Conference, St. Louis, MO

• April 2017: PDE and Differential Geometry Seminar, U. Connecticut

• March 2017: UConn Math Club, U. Connecticut

• January 2016: The 2016 Joint Math Meetings – AMS Special Session on Geometry and Differential Geometry, Seattle, WA

• September 2015:  STEM Faculty Launch Research Talk, Worcester Polytechnic Institute

• October 2014: 2014 AMS Fall Western Sectional Meeting – AMS Contributed Talk, San Francisco State U.

• August 2014: Pure Mathematics Topology and Geometry Seminar, U. Waterloo

• September 2014: AMS Graduate Student Reading Seminar, U. Houston

• April 2014: AMS/SIAM Graduate Student Paper Presentations, U. Houston

• March 2014: Seminar on Complex Geometry & Complex Analysis, U. Houston

• April 2013:  Seminar on Complex Geometry & Complex Analysis, U. Houston

• April 2012: Seminar on Complex Geometry & Complex Analysis, U. Houston

• March 2011: Pi Mu Epsilon Undergraduate Research Presentation, U. Houston

Summer Programs and Workshops:​

• [July 2024]: Collaborate@ICERM, Institute for Computational and Experimental Research in Mathematics, Providence, RI

• [June 2024]: AIM’s SQuaREs Research Program, American Institute of Mathematics, Pasadena, CA

• July 2023:  MAA Open Math Summer Workshop: Engaging Multivariable Calculus Students using CalcPlot3D and 3D-Printed Surfaces {Virtual}

•  July 2023: Summer Research in Mathematics (Invited Researcher), Simons Laufer Mathematical Sciences Institute

• August 2022: C.O.U.R.A.G.E. (Challenging, Operationalizing, and Understanding Racialized and Gendered Events) in Undergraduate Mathematics Workshop, {Virtual}

• July 2022: Deep Teaching Residency (DTR) Faculty Development Program, HHMI

• July 2022: Lean for the Curious Mathematician 2022 Workshop, ICERM

• September 2021: Embodied Mathematical Imagination and Cognition: Professional Development for Undergraduate Mathematics Instructors, Colorado State University {Virtual}

• June 2021: Latinx Mathematicians Research Community (LMRC), American Institute of Mathematics {Virtual}

• {July 2020}: Undergraduate Faculty Research Program, IAS &PCMI - postponed due to COVID-19

• July 2020: Online Pedagogy: Design for Online Learning Week-long Course, SUNY Potsdam

• June 2019: R.E.U.F. Continuation at the Institute for Computational and Experimental Mathematics (ICERM), Providence, RI

• June 2018: Academy of IBL, MAA Carriage House Workshop, Washington, D.C.

• June 2018: R.E.U.F. at American Institute of Mathematics (A.I.M.), San Jose, CA

• June 2017:  Workshop on Increasing Minority Participation in Undergraduate Mathematics, PCMI, Park City, UT

• October 2016: NES MAA Workshop: Teaching Calculus Now, St. Michael's College, VT

• September 2015: STEM Faculty Launch, Worcester Polytechnic Institute

• July 2015: The Graduate Student Bootcamp for the 2015 Summer Research Institute on Algebraic Geometry, U. Utah

• May 2015: Women and Math Program, “Aspects of Algebraic Geometry”, Institute for Advanced Study & Princeton U.

• March 2015: Workshop for Underrepresented Groups in Academia, IMA & U. Minnesota

Conferences Attended:

• [August 2024]: MAA MathFest, Indianapolis, IN

• [July 2024]: Building Thinking Classrooms Summer Conference 2024, Phoenix, AZ

• January 2024: 2024 Joint Mathematics Meetings, San Francisco, CA

• November 2023: The 2023 Arizona Women's Symposium in Mathematics (AWSiM II) - Northern Arizona University (Organizer and Co-Director)

• August 2023: The Ninth Annual Conference for the Exchange of Mathematical Ideas, U. of Northern Iowa 

• August 2023: MAA MathFest, Tampa, FL

• May 2023: Mathematical Pathways to an Excellent Future, U. of California Riverside

• May 2023: 2023 AMS Spring Western Sectional Meeting, Fresno State U.

• November 2022: The Arizona Women's Symposium in Mathematics (AWSiM) - Embry-Riddle Aeronautical University, Prescott (Lead-Organizer and Co-Director)

• August 2022: The Eighth Annual Conference for the Exchange of Mathematical Ideas,  ERAU Prescott

• August 2022: MAA MathFest, Philadelphia, PA

• March 2022: Midwest Geometry Conference 2022, Wichita State University

• March 2022: Critical Issues in Mathematics Education 2022: Initiating, Sustaining, and Researching Mathematics Department Transformation of Introductory Courses for STEM Majors, Mathematical Sciences Research Institute

• April 2022: ArizMATYC/MAA Southwestern Section Joint Conference, Arizona State U. Polytech

• February 2022: Texas Geometry & Topology Conference 2022, University of Texas at Dallas

• April 2019: MAA Seaway Section Meeting, St. John Fisher College

• March 2019: AMS Spring Central & Western Joint Sectional Meeting, U. Hawaii at Manoa

• January 2019: 2019 Joint Math Meetings, Baltimore, MD

• August 2018: MAA MathFest, Denver, CO (Project NExT Fellow)

• April 2018: MAA Seaway Section meeting, SUNY Brockport

• February 2018: The 2018 Texas Geometry and Topology Conference, U. Houston

• January 2018: 2018 Joint Math Meetings, San Diego, CA (Project NExT Fellow)

• November 2017: Math Alliance: 2017 National Field of Dreams Conference, St. Louis, MO

• October 2017: MAA Seaway Section/NYSMATYC Meeting, SUNY Broome

• July 2017: MAA MathFest, Chicago, IL (Project NExT Fellow)

• April 2017:  Algebraic Geometry Northeastern Series 2017, Stony Brook U.

• March 2017:  Georgia Algebraic Geometry Symposium 2017, U. Georgia

• January 2016: 2016 Joint Math Meetings, Seattle, WA

• July 2015: 2015 Summer Research Institute on Algebraic Geometry (Week 1), U. Utah

• April 2015: Texas Algebraic Geometry Symposium 2015, Texas A&M U.

• February 2015: 51st Annual Texas Geometry & Topology Conference, U. Houston

• January 2015: 2015 Joint Math Meetings, San Antonio, TX

• October 2014: 2014 AMS Fall Western Sectional Meeting, San Francisco State U.

• April 2013: 11th Annual Graduate Student Topology & Geometry Conference, U. Notre Dame

• September 2012: The Topology of Algebraic Varieties, CRM at U. Montreal

• April 2012: Texas Algebraic Geometry Symposium 2012, Texas A&M U.

• February 2012: 47th Annual Texas Geometry & Topology Conference, U. Houston

• October 2010: National Alliance Field of Dreams Conference, U. Iowa